Question: Factor completely. $2x^2-50=$
Answer: First, we take a common factor of $2$. $2x^2-50=2(x^2-25)$ Now, let's factor $x^2-25$. Both $x^2$ and $25$ are perfect squares, since $x^2=({x})^2$ and $25=({5})^2$. $x^2-25 = ({x})^2-({5})^2$ So we can use the difference of squares pattern to factor. ${a}^2 - {b}^2 =({a}+{b})({a}-{b})$ In this case, ${a}={x}$ and ${b}={5}$ : $({x})^2 - ({5})^2 =({x}+{5})({x}-{5})$ $\begin{aligned} 2x^2-50&=2(x^2-25) \\\\ &=2(x+5)(x-5) \end{aligned}$ In conclusion, the complete factorization is: $2(x+5)(x-5)$ Remember that you can always check your factorization by expanding it.